The fuses (plural) in question are on the backlight inverter board.
They will be surface mount fuses that are approximately 0.062-.125
inches long. Each backlight inverter circuit on the board (count the
transformers) will probably have a fuse on the power line going to that
part of the circuit. If any of the inverters does not run, the whole
thing shuts down.

Most of the monitors will restart the inverters during screen
resolution change, and you may see a short flash of video for less than
a second. This is the common symptom when one of the inverter fuses
opens up on a multi-inverter, multi-lamp unit.

If you are not equipped and experienced working with the ultra small
surface mount components, you may want to practice and get the correct
soldering iron tip and solder for the job.